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2L 4s: Difference between revisions

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{{Infobox MOS
{{Infobox MOS
| Name = antilemon
| Name = malic
| Periods = 2
| Periods = 2
| nLargeSteps = 2
| nLargeSteps = 2
| nSmallSteps = 4
| nSmallSteps = 4
| Equalized = 1
| Equalized = 1
| Paucitonic = 0
| Collapsed = 0
| Pattern = LssLss
| Pattern = LssLss
}}
}}


The only scale with this [[MOSScales|MOS]] pattern that's a really significant minimum of harmonic entropy is [[Diaschismic_family|srutal/pajara]], in which the period plus the generator is 3/2. Other scales include shrutar, in which the generator is '''half''' of that (about a quartertone), so 3/2 is a period plus two generators; and [[Porcupine_family#Hedgehog|hedgehog]], in which two generators make a 6/5, and 4/3 would be three generators (except that it doesn't appear in this MOS).
{{MOS intro}}
 
The only scale with this [[MOSScales|MOS]] pattern that's a really significant minimum of [[harmonic entropy]] is [[Diaschismic_family|srutal/pajara]], in which the period plus the generator is 3/2. Other scales include [[shrutar]], in which the generator is '''half''' of that (about a [[quartertone]]), so 3/2 is a period plus two generators; and [[Porcupine_family#Hedgehog|hedgehog]], in which two generators make a 6/5, and 4/3 would be three generators (except that it doesn't appear in this MOS).


In addition to the true MOS with pattern LssLss, all these scales also come in a near-MOS version, LsLsss, in which the period is the only generic interval that has more than two specific representatives.
In addition to the true MOS with pattern LssLss, all these scales also come in a near-MOS version, LsLsss, in which the period is the only generic interval that has more than two specific representatives.
Line 15: Line 17:
Srutal/pajara probably has the lowest harmonic entropy of all 6-note MOS scales. The near-MOS version has even lower harmonic entropy.
Srutal/pajara probably has the lowest harmonic entropy of all 6-note MOS scales. The near-MOS version has even lower harmonic entropy.


{| class="wikitable"
== Scale properties ==
|-
{{TAMNAMS use}}
! colspan="11" | Generator
 
! | Cents
=== Intervals ===
! | Comments
{{MOS intervals}}
|-
 
| | 0\2
=== Generator chain ===
| |
{{MOS genchain}}
| |
 
| |
=== Modes ===
| |
{{MOS mode degrees}}
| |
 
| |
== Scale tree ==
| |
{{MOS tuning spectrum
| |
| 9/7 = [[Unidec]]
| |
| 13/8 = Golden [[hedgehog]]/[[echidna]]
| |
| 5/3 = Hedgehog (optimal around here)
| | 0
| 9/4 = [[Crepuscular]]
| style="text-align:center;" |
| 8/3 = [[Octokaidecal]]
|-
| 7/2 = [[Pajara]]
| |
| 9/2 = [[Injera]]
| |
| 6/1 = [[Shrutar]] ↓
| |
}}
| |
| |
| |
| |
| |
| |
| | 1\24
| |
| | 50
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| | 2\46
| | 52.17
| style="text-align:center;" | Shrutar is around here
|-
| |
| |
| |
| |
| |
| |
| |
| |
| | 1\22
| |
| |
| | 54.55
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| |
| | 1\20
| |
| |
| |
| | 60
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| | 1\18
| |
| |
| |
| |
| | 66.67
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| | 1\16
| |
| |
| |
| |
| |
| | 75
| style="text-align:center;" |
|-
| |
| |
| |
| |
| | 1\14
| |
| |
| |
| |
| |
| |
| | 85.71
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| | 2\26
| |
| |
| |
| |
| |
| | 92.31
| style="text-align:center;" | Injera is around here
|-
| |
| |
| |
| | 1\12
| |
| |
| |
| |
| |
| |
| |
| | 100
| style="text-align:center;" | L/s = 4
|-
| |
| |
| |
| |
| | 2\22
| |
| |
| |
| |
| |
| |
| | 109.09
| style="text-align:center;" | Srutal/Pajara is around here
|-
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| | 600/(2+pi)
| |
|-
| |
| |
| | 1\10
| |
| |
| |
| |
| |
| |
| |
| |
| | 120
| style="text-align:center;" | L/s = 3
|-
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| | 600/(2+e)
| |
|-
| |
| |
| |
| |
| | 3/28
| |
| |
| |
| |
| |
| |
| | 128.57
| |
|-
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| | 600/(3+phi)
| |
|-
| |
| |
| |
| | 2/18
| |
| |
| |
| |
| |
| |
| |
| | 133.33
| |
|-
| |
| | 1\8
| |
| |
| |
| |
| |
| |
| |
| |
| |
| | 150
| style="text-align:center;" | Boundary of propriety (generators


larger than this are proper)
[[Category:6-tone scales]]
|-
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| | 600/(2+sqrt(3))
| |
|-
| |
| |
| |
| | 3\22
| |
| |
| |
| |
| |
| |
| |
| | 163.64
| style="text-align:center;" | Hedgehog and echidna are both around here
|-
| |
| |
| |
| |
| |
| | 8\58
| |
| |
| |
| |
| |
| | 165.52
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| | 600/(2+phi)
| style="text-align:center;" | Golden hedgehog/echidna
|-
| |
| |
| |
| |
| |
| |
| | 13\94
| |
| |
| |
| |
| | 165.96
| style="text-align:center;" |
|-
| |
| |
| |
| |
| | 5\36
| |
| |
| |
| |
| |
| |
| | 166.67
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| | 600/(2+pi/2)
| |
|-
| |
| |
| | 2\14
| |
| |
| |
| |
| |
| |
| |
| |
| | 171.43
| style="text-align:center;" | Optimum rank range (L/s=3/2)
|-
| | 1\6
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| | 200
| style="text-align:center;" |
|}
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